A multi-faceted research project aimed at developing the capacity for theoretical characterization of biophysical interactions and enzyme-catalyzed reactions in solution is proposed. The theoretical approach centers on computer simulations of enzymatic systems, using combined quantum mechanical and molecular mechanical (QM/MM) methods. To increase the accuracy of the computational methods, a generalized hybrid orbital (GHO) approach will be developed at the ab initio molecular orbital level to treat the covalent bond division between quantum- mechanical and classical fragments. In addition, an ab initio mixed molecular orbital-valence bond (MOVB) method is being developed to treat the solvent reaction coordinate for solution and enzymatic reactions. This approach goes beyond the traditional empirical valence bond (EVB) method where empirical force fields are used to calibrate parameters for the diabatic reactant and product states. A major thrust is to investigate the mechanism of enzyme- catalyzed reactions using combined QM/MM methods. In particular, the dephosphorylation reaction of human protein tyrosine phosphatase 1B (PTP1B) and the squalene to hopene conversion by squalene cyclase will be studied to provided a detailed understanding of substrate binding, reaction mechanism, and free energy profiles for the enzymatic process. PTP1B is found in a variety of human tissues, which is overexpressed in breast-cancer and has a major role in both insulin sensitivity and fuel metabolism. Computational studies of these enzyme reactions can help to better design cholesterol-lowering drugs and therapeutic agents for treatment of cancer, diabetes and obesity. In addition, the vibrational population relaxation of an azide ion in the active site of carbonic anhydrase II will be investigated to understand the relationship between enzyme reactivity and protein dynamics and fluctuation. The vibrational relaxation time and vibrational frequency-frequency correlation function will be computed to help interpret recent laser spectroscopic experiments.